Various techniques may be used to evaluate geological formations. For example, measurements may be made using tools located within a borehole such as in support of geophysical and petrophysical exploration or resource extraction. In one approach, an acoustic or “sonic” logging technique is used. A transducer is located in the borehole and is electrically driven to insonify a region nearby the transducer. Insonification induces propagating acoustic waves in the borehole, within the geologic formation through which the borehole extends, or along the interface between the geologic formation and the borehole.
In one approach, a monopole acoustic transducer is used. The monopole acoustic transducer generally emits an acoustic wavefront having spherical or cylindrical uniformity. Such a symmetric wavefront induces a compressive wavefront or “P-wave.” A portion of the P-wave is reflected by the interface between the borehole and the formation at the borehole wall, and a portion of the P-wave is refracted within the formation. As the propagation direction of the refracted portion of the P-wave converges on the borehole-formation interface, a portion of the refracted P-wave energy is transferred back into the borehole (e.g., a first “head wave”). Reflected or refracted waves are then detected at respective locations remotely with respect to the transmitting transducer, such as a few meters or tens of meters away, providing information about the propagation characteristics of the formation (and thus information indicative of formation composition or porosity). A time difference between arrivals of the P-waves at respective transducers is divided by a distance between the transducers to obtain a “slowness” parameter, having units that represent an inverse of velocity (e.g., microseconds per foot or microseconds per meter).
A transverse or shear wavefront, referred to as an “S-wave,” may also be induced in the formation by a monopole transducer, if the formation supports a shear wave speed faster than the velocity of a wave traveling exclusively in the fluid surrounding the borehole (e.g., a “mud wave”). When this condition is met, the formation is referred to as a “fast formation.” The S-wave is similarly refracted toward the borehole-formation interface, and is detected at the respective remote locations typically following the refracted P-wave. In this manner, “shear slowness” is then determined using the time difference between arrivals of a shear wave signature at respective receiving transducers, divided by the distance between the transducers.
Other acoustic propagation modes are also supported, such as a surface wave at the borehole-formation interface, referred to as a “Stoneley wave.” The arrival of the Stoneley wave at the receiving transducers generally occurs after the refracted P-wave and S-wave arrivals, and the Stoneley wave exhibits a varying degree of penetration into the formation and a slightly varying propagation velocity depending on the frequency of acoustic energy. Information about such frequency dependence or “dispersion” is used to provide information about formation permeability.
Monopole transducers provide only a limited range of acoustic modes that can be launched into the formation depending on the formation properties and only a limited range of frequencies of acoustic radiation. For example, monopole acoustic transducers may be unsuitable as a transmission source for measurement of shear slowness in “slow” formations (e.g., where a shear wave propagation velocity is slower in the formation than in the fluid filling the borehole). Monopole transducers may also be unsuitable for determination of shear wave anisotropy with respect to rotational position or azimuth around a circumference of the borehole, or for determination other parameters such as flexural wave dispersion for “slow” formations.